Breaking symmetries for equivariant coarse homology theories

TL;DR

This paper introduces a symmetry breaking method in coarse geometry to analyze equivariant coarse homology classes, providing new insights and applications, especially in spectral theory of invariant differential operators.

Contribution

It presents a novel symmetry breaking construction in coarse geometry and offers an analytic interpretation for equivariant coarse K-homology, with applications to spectral theory.

Findings

Enables analysis of equivariant coarse homology via restriction to smaller groups

Provides an analytic interpretation of equivariant coarse K-homology

Applications to the spectral theory of invariant differential operators

Abstract

We describe a symmetry breaking construction in coarse geometry which allows to obtain information about equivariant coarse homology classes by restriction to smaller groups and spaces. In the case of equivariant coarse $K$-homology theory we give an analytic interpretation of this construction. As a consequence we obtain applications to the spectral theory of invariant differential operators.